Fifth Week Final Test

$F(x)$ has no discontinuities for all points in the domain of $f(x)$ ;

Correct

Correct!

the domain of $F(x)$ is included in the domain $f(x)$ ;

the antiderivative for $f(x+C)$ is $F(x+C)$ ;

Correct

Correct!

$F(x)$ is also an antiderivative for $f(x)+C$ ;

the domain of $f(x)$ coincides with the domain of $F(x)$ ;

- \frac{4}{3}

-4/3

Correct

The indefinite integral is $F(x)=\frac{2}{3}(x-3)\sqrt{x}+C$ .

- \frac{2}{3}

-2/3

Correct

0.5

.5

Correct

2

2

Correct

let $f(x)>g(x)$ and integral $\int_a^{+\infty} f(x) dx$ converges; than $\int_a^{+\infty} g(x) dx$ also necessarily converges;

if $f(x)$ is integrable over any finite segment, than the convegence of improper integral is equivalent to the existence of the limit of its antidervative $F(x)$ as $x$ approaches $+\infty$ ;

Correct

it is possible that one can compute $\int_a^{+\infty} f(x) dx$ , but the integral does not converge;

1

1

Correct

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